Null spaces and ranges of polynomials of operators

• Autores: Manuel González Ortiz
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 32, Nº 2, 1988, págs. 167-170
• Idioma: inglés
• DOI: 10.5565/publmat_32288_04
• Títulos paralelos:
  • Especies nulas y rangos de polinomios de operadores
• Enlaces
  • Texto completo
• Resumen

  • We give an elementary proof of the fact that given two polynomials P, Q without common zeros and a linear operator A, the operators P(A) and Q(A) verify some properties equivalent to the pair (P(A),Q(A)) being non-singular in the sense of J.L. Taylor. From these properties we derive expressions for the range and null space of P(A) and spectral mapping theorems for polynomials fo continuous (or closed) operators in Banach spaces.